A particular kind of die has eight faces with the numbers 1, 2, 3, 4, 5, 6, 7, B. Rolling the die means any of the eight numbers can come up with equal probability. When | refer to a "die" below, that's the kind I'm talking about. In what follows we will always roll the die six times in succession. a) How many different sequences of numbers are possible when we roll the die six times in succession? Here are examples of three different sequences to illustrate: 3.4,3,6,7,1, 2,56,55,8 4,1,6,3,7.3 b) How many of the sequences have exactly three sevens? Here are examples to illustrate: 4,3,7,8,7,7 7,7,7,2,3,1 7,6,8,7,57 c) How many of the sequences have at least four sevens? Here are examples to illustrate: 7,8,7,3,7,7 77T 7,7,6,7,7,7 d) How many sequences have at most two sevens? Here are examples to illustrate: 6,8,1,3,7,7 2,2,5,4,8,7 6,5,4,3,2,5 ) What are the probabilities for each of the events in Parts b, and d? Also, how are the three probabilities related? Justify your answers. f) What is the probability of getting a total of at least 467 g) How many of the sequences have exactly the same number of 7's and 8's ? h) Suppose we group the possible sequences into categories according to how many of each number occurred. For example 6, 6,7, 3, 3, 6 would be in the same category as 7, 6, 3, 6, 3, 6 since both sequences have three &'s, two 3's and one 7. How many such categories are possible? Carefully justify your